What Can An In-Running Model Reveal About Close Games?

There are, clearly, a lot of people who are firmly convinced that some teams win a greater or lesser share of close games than they "should".

Whilst no statistical model can provide any meaningful perspective on whether a single outcome was or was not due solely or mostly to chance, a model can provide some quantitative information about how plausible a chance explanation might be.

I have in the past written about this topic in the context of the proportion of games finishing with a given margin (or less) that a team of specified pre-game superiority might be expected to win. There I found, for example, that a 3-goal pre-game favourite should be expected to win games decided by 3-goals or less about 55% of the time.

That analysis provided a post hoc view, looking at games that finished as close games. For today's post on this topic I'm going to adopt an in-running view, drawing on a simplified version of a model similar I derived in this post, looking at games that were close with some, limited time remaining.

The simplified model is also built using data from the period 2008 to 2016 and produces fitted values that correlate about +0.99 with those from the more complex model at all points in the game.

It is, like the more complex model, a quantile regression model of the form:

Predicted Final Home Margin = a₀ + a₁ Current Home Lead / ((1 - Game Fraction)^-0.03) + a₂ (1- Game Fraction)^1.16 + a₃ Pre Game Home Probability (1 - Game Fraction)^1.20

The exponents in this model were selected to minimise the Akaike Information Criterion (which was 1,643,364 for the simpler model compared to 1,643,134 for the more complex model). The fitted values of a0, a1, a2, and a3 depend on the particular quantile chosen, and the model was fitted to quantiles in 1% increments from 1% to 99%. In fitting the model, the pre-game home team probabilities were estimated from the pre-game TAB head-to-head prices (using the overround equalising methodology).

Using this model we can ask the following question: for a home team with a specified pre-game probability of victory and a given lead with X% of the game to go, what is the fitted probability that the home team wins?

By constraining the size of the given lead and the fraction of the game remaining to relatively small values, we can explore the in-running model's views of what would be considered "close games".

Specifically, we're going to look at games where the lead, from the home team perspective, was been -3 and +3 goals, and where there was either 5% (about 6 minutes) or 10% (about 12 minutes) of the game remaining.

The in-running model outputs for these scenarios appear below.

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On the left we have the results for games with about 12 minutes remaining and where the lines relate to home teams assessed as having pre-game victory probabilities of either 10%, 30%, 50%, 70% or 90%. We see there, for example, that a 70% pre-game home team favourite tied with 12 minutes to go has about a 55% probability of victory.

As well, we see that a 90% pre-game favourite trailing by a couple of points with 12 minutes remaining is still a narrow favourite.

With only 6 minutes remaining, however, leads become far more important, even for underdogs. For example, a home team assessed as just 10% chances pre-game are over 70% favourites if they lead by a goal at that point, and about 90% favourites if they lead by 2 goals.

The broader conclusions from the chart are that:

• Teams assessed as strong pre-game favourites will have a substantially higher likelihood of winning games that are close with 12 minutes remaining than will teams assessed as large pre-game underdogs. A 90% pre-game favourite will have about a 25% point higher probability of winning a game tied with 12 minutes to go than will a 10% pre-game underdog.
  Even 90% pre-game favourites that trail by 6 points with 12 minutes remaining will have more than a 15% point higher victory probability than teams that were 10% pre-game underdogs and trailed by the same amount. 
• The advantage that stronger teams have over weaker ones dissipates somewhat - but still remains - when we look, instead, at the situation with 6 minutes remaining. For example, a tied game at that point would see a 90% pre-game favourite still 15% points more likely to win than a 10% pre-game favourite.

In short, better teams will tend to win more close games than weaker teams, but at an incremental rate lesser than their pre-game probability would have indicated, much lesser if the game remains close as it enters its final minutes, and lesser still if the better team trails. A tied game, however, is only a 50:50 proposition for a team that was a 50:50 proposition when the game commenced.